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1 results

  • A characterization of the uniform distribution on the circle in the analysis of directional data

  • M. S. Bingham
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 4 / December 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 852-857
    Print publication:
    December 1978

  • It was conjectured some time ago by K. V. Mardia that if, for random samples of some fixed size N ≧ 2 from a given non-degenerate circular population, the sample mean direction and the sample resultant length are independently distributed, then the population must be uniformly distributed round the circle. In this paper it is shown that, apart from one minor exception, Mardia's conjecture is true in the case N = 2. No regularity conditions are necessary for the proof. The same problem has been studied, subject to regularity conditions, by Kent, Mardia and Rao (1976) for all sample sizes N ≧ 2 except N = 4.